The shift from small, independent family farms to fewer, larger farms that rely heavily upon capital and technology began in 1793 with the invention of the cotton gin. The cotton gin enabled a single farm worker to clean 1,000 pounds of cotton in a day—a tremendous increase from the 50 pounds daily that an individual could clean without the gin. The continual adoption of new technologies in agriculture, along with the application of genetics, chemistry, physics, biology, and plant and animal nutrition, has created an agricultural industry in which mathematics play an increasingly important role.

Crop Production Planning Models

Because most soils and climates are suitable for producing a variety of agricultural products, many farmers build a mathematical model to determine what crops to plant in which fields. Whereas some costs included in the model, such as insurance, taxes, depreciation, interest, land rents, and loan payments, are fixed, others vary...